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Topologically invariant σ-ideals on the Hilbert cube

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Abstract

We study and classify topologically invariant σ-ideals with Borel base on the Hilbert cube and evaluate their cardinal characteristics. One of the results of this paper solves (positively) a known problem whether the minimal cardinalities of the families of Cantor sets covering the unit interval and the Hilbert cube are the same.

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Authors and Affiliations

  1. Department of Mathematics, Ivan Franko National University of Lviv, Lviv, Ukraine

    Taras Banakh

  2. Institute of Mathematics, Jan Kochanowski University, Kielce, Poland

    Taras Banakh

  3. Institute of Mathematics and Computer Science, Wrocław University of Technology, Wrocław, Poland

    Michał Morayne, Robert Rałowski & Szymon Żeberski

Authors
  1. Taras Banakh
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  2. Michał Morayne
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  3. Robert Rałowski
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  4. Szymon Żeberski
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Corresponding author

Correspondence to Taras Banakh.

Additional information

The work has been partially financed by NCN means granted by decision DEC-2011/01/B/ST1/01439.

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Banakh, T., Morayne, M., Rałowski, R. et al. Topologically invariant σ-ideals on the Hilbert cube. Isr. J. Math. 209, 715–743 (2015). https://doi.org/10.1007/s11856-015-1235-z

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  • DOI: https://doi.org/10.1007/s11856-015-1235-z

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